Given that point A and point B are two fixed points ON the edge ON of ∠MON, point C is the fixed point on the edge OM, and when c is located, ∠ACB is the largest? In the process of investigating the maximum value of junior high school, Miller's problem has also become the problem of maximum opening angle or maximum perspective.

Miller Theorem: It is known that point AB is two fixed points ON the edge ON of ∠MON and point C is a fixed point on the edge OM, then ∠ACB is maximum if and only if the outer circle of triangle ABC is tangent to the edge OM.

Miller, a famous German mathematician (1436- 1476), studied trigonometry and astronomy at Leipzig University and Vienna University successively, and was a professor at Vienna University from 1468 to 147 1 year. 147 1 settled in Nuremberg and engaged in astronomical research. Miller made a great contribution to trigonometry. From about 146 1 to 1464, he wrote on the triangle. The book is divided into five volumes, the first two volumes are about plane triangles, and the last three volumes are about spherical triangles.

In the book, the sine theorem and cosine theorem of Spherics are given, and an accurate trigonometric function table is calculated. These works make trigonometry separate from astronomy and become an independent discipline, so Miller is considered as the most influential mathematician in Europe since Fibonacci.

In 147 1, Miller asked Professor Naugle an interesting question: Where on the earth's surface is the longest vertical pole (that is, the place with the largest viewing angle). This maximum perspective problem is called "Miller Problem" and its conclusion is called "Miller Theorem", which is also the first extreme value problem among 100 famous extreme value problems in the history of mathematics.